From 76ba6248f5f6a0cd87c5262973cf76d8682d9d6a Mon Sep 17 00:00:00 2001 From: Damaris Parasca <126685870+damarisparasca@users.noreply.github.com> Date: Wed, 17 Sep 2025 13:51:10 +0100 Subject: [PATCH 1/9] made a change --- .DS_Store | Bin 6148 -> 6148 bytes problemSets/.DS_Store | Bin 0 -> 6148 bytes problemSets/example/PS01_answersJZ.R | 2 +- 3 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 problemSets/.DS_Store diff --git a/.DS_Store b/.DS_Store index 9fce2b5eed715c12ff333ab60b7fcfe5a98f1baa..96b24b2678e22f8b7281191d644085db522db6d9 100644 GIT binary patch delta 169 zcmZoMXfc=|#>B!ku~2NHo}wrV0|Nsi1A_nqLk>eKLoP!wkSy6O$h@3c5+udVP{2^c zkk62WEInC)sY%4h+*C)w*xaI4N1@u%$UsNI#Mo@|HYQ_btXdd~%YuvYa`N-iLH2Ft kVfxOrnVo~51LzQ-W#5@6^NTog0Nud^lxEl*A+m-U0779R$^ZZW delta 85 zcmZoMXfc=|#>B)qu~2NHo}wrd0|Nsi1A_nqLlHwJLn1>CLvd31#=_-{lMO^zHVdS5T3QwrWBzEg&r5Y7ObsW#Y?F51&ruHr6x3JFwK^xwL&T6tS{t~_&m<+ zZop~}o4~LeDXT7{Xwh4ug2f zM1Rpl-(G?cp23F!eENPBpyw?Z#!)(MG~UHpp}4+La!O9cx%D2@)EoQbN!sy8*EG6N zDh_hp4=$r{+N*Azs$}d(NjTC8Q9s0xo2w}4t7%6~l76alJ>zi7PPtdD&1TK^L0z`m zNAtRz9XA_wx!*dR&&$sC&hE*1?=c=E>cvngkaaDa7ISz-TnRQLGGCWW?+$lf*Drn z{6E8AX6Yk;F@;CW05kB<7!bv-*X>|Y_H6xD9-Xxk+Z{F%ipxkrL4Dy8fCJh`YT9Z1 bl5~u7EoKI37P9MfM7{`ULbziFeu04xc*jhf literal 0 HcmV?d00001 diff --git a/problemSets/example/PS01_answersJZ.R b/problemSets/example/PS01_answersJZ.R index 9603507..a63c064 100644 --- a/problemSets/example/PS01_answersJZ.R +++ b/problemSets/example/PS01_answersJZ.R @@ -3,7 +3,7 @@ # set wd # clear global .envir ##################### - +x <- 3 # remove objects rm(list=ls()) # detach all libraries From d282dfd59b5e417623e9d355bfac8673b1cb2e32 Mon Sep 17 00:00:00 2001 From: Damaris Parasca <126685870+damarisparasca@users.noreply.github.com> Date: Wed, 24 Sep 2025 13:04:38 +0100 Subject: [PATCH 2/9] update --- problemSets/example/.RData | Bin 0 -> 49 bytes problemSets/example/.Rapp.history | 0 problemSets/example/.Rhistory | 2 ++ 3 files changed, 2 insertions(+) create mode 100644 problemSets/example/.RData create mode 100644 problemSets/example/.Rapp.history create mode 100644 problemSets/example/.Rhistory diff --git a/problemSets/example/.RData b/problemSets/example/.RData new file mode 100644 index 0000000000000000000000000000000000000000..22710ecc516e949f624fc2728e5ea12575cce7dd GIT binary patch literal 49 zcmb2|=3oE=X6~X+gJ)e2k`fXU(h?F=QxeixjU*$So$r+BHuTgp#4bJLqX1M109h{% A+5i9m literal 0 HcmV?d00001 diff --git a/problemSets/example/.Rapp.history b/problemSets/example/.Rapp.history new file mode 100644 index 0000000..e69de29 diff --git a/problemSets/example/.Rhistory b/problemSets/example/.Rhistory new file mode 100644 index 0000000..126aa8a --- /dev/null +++ b/problemSets/example/.Rhistory @@ -0,0 +1,2 @@ +demo() +q() From f3acc0d724b04f23eebdfefebac5b6e3e9a358f1 Mon Sep 17 00:00:00 2001 From: Damaris Parasca <126685870+damarisparasca@users.noreply.github.com> Date: Tue, 30 Sep 2025 10:53:30 +0100 Subject: [PATCH 3/9] Create .Rapp.history --- tutorials/Wednesday/Week 2/.Rapp.history | 25 ++++++++++++++++++++++++ 1 file changed, 25 insertions(+) create mode 100644 tutorials/Wednesday/Week 2/.Rapp.history diff --git a/tutorials/Wednesday/Week 2/.Rapp.history b/tutorials/Wednesday/Week 2/.Rapp.history new file mode 100644 index 0000000..112c1ff --- /dev/null +++ b/tutorials/Wednesday/Week 2/.Rapp.history @@ -0,0 +1,25 @@ +rm(list=ls()) +detachAllPackages <- function() {# + basic.packages <- c("package:stats", "package:graphics", "package:grDevices", "package:utils", "package:datasets", "package:methods", "package:base")# + package.list <- search()[ifelse(unlist(gregexpr("package:", search()))==1, TRUE, FALSE)]# + package.list <- setdiff(package.list, basic.packages)# + if (length(package.list)>0) for (package in package.list) detach(package, character.only=TRUE)# +}# +detachAllPackages()# +# +# Load libraries# +pkgTest <- function(pkg){# + new.pkg <- pkg[!(pkg %in% installed.packages()[, "Package"])]# + if (length(new.pkg)) # + install.packages(new.pkg, dependencies = TRUE)# + sapply(pkg, require, character.only = TRUE)# +}# +# +# Load any necessary packages# +lapply(c("readr", "ggplot2", "dplyr", "viridis"), pkgTest)# +# +# Get working directory# +getwd() +setwd("/Users/elkarag/Desktop/Teaching/Applied Stats I") +setwd("/Users/elkarag/Desktop/Teaching/Applied Stats I") +df <- read_csv("fictional_data.csv") From 7775629918948b10dadf0015c14894cc31ac32d4 Mon Sep 17 00:00:00 2001 From: Damaris Parasca <126685870+damarisparasca@users.noreply.github.com> Date: Tue, 7 Oct 2025 19:50:06 +0100 Subject: [PATCH 4/9] updates --- .DS_Store | Bin 6148 -> 8196 bytes .gitignore | 1 + problemSets/.DS_Store | Bin 6148 -> 8196 bytes problemSets/PS01/template/.RData | Bin 0 -> 6004 bytes problemSets/PS01/template/.Rhistory | 512 +++++++++++++++++++++++ problemSets/PS01/template/PS01.R | 125 +++++- problemSets/PS01/template/PS01.log | 75 ++++ problemSets/PS01/template/PS01.tex | 2 +- problemSets/PS01/template/template.Rproj | 13 + problemSets/answers_DP/PS01_DP.R | 165 ++++++++ problemSets/answers_DP/PS01_DP.aux | 0 problemSets/answers_DP/PS01_DP.tex | 130 ++++++ 12 files changed, 1021 insertions(+), 2 deletions(-) create mode 100644 problemSets/PS01/template/.RData create mode 100644 problemSets/PS01/template/.Rhistory create mode 100644 problemSets/PS01/template/PS01.log create mode 100644 problemSets/PS01/template/template.Rproj create mode 100644 problemSets/answers_DP/PS01_DP.R create mode 100644 problemSets/answers_DP/PS01_DP.aux create mode 100644 problemSets/answers_DP/PS01_DP.tex diff --git a/.DS_Store b/.DS_Store index 3357b22c8aab880baf43ce4f1a1cf3e56ad20917..1b6e70b2ed199b686e5a5c37a20b7d818ae105b2 100644 GIT binary patch literal 8196 zcmeHMO-~a+7=EXqY{id7K+$Nju@@7G@)ZIx##$g+zaW$-2wHcyLs?yBn%yl`2}#eI zc<|^C@CSJE=*6Q~4_^EO9z1!~cRtETfoQyFWZq=vc{}qyvz=%A?#yfffaI#Bet;eT zu&@ZU+p*fgM87E8ETvlnk02i)1_}wp`H=hDqD_NQz$jo8FbWt2i~|3H0=Q-ivvyhc zRj;Xy0!D#7sepJsI9LQ`HP#i%M+a8&2!Pm%&C<}vbAaSH8nYVf3MCcCRHp}`sYD+! zh@xY^Bf=508tV!b9f+a>(N`w=ghJ%ik>|*8AX$Z`HVPO8wksgkehW(A;>#U9r^z}MJgTrfUX{$SP;o@}hak$L*bDRkp(GNN}q&~0L zFVNdXlfYlmvm+lHv-@J(jrpYyv>!Zl_=w$cw6mkDqr1EN*zukdCr_R#+MS;3KQ2e& zdynyuN4c;{X9J(JLhy{vCiF=noT7cSDQ=pU9&9wtJgs0%*G7XJ>uN+Pn=eN}X>xHf zrpfFkf39dBiT#L&;S`U9B;agrAx6pb30=;!MUGcoLAfU@qAR{bqZn};XLinwBA1nE z?&v7UVCBr^Z%WimcBXFPTvHxhEzSuK3SRP^#CgSP}B?T)HBHHC~ j9C7^*L-ZZpm(^HTh&^b3>qWp$+iJ7^%UfcqJ)po(4?1fw delta 145 zcmZp1XfcprU|?W$DortDU=RQ@Ie-{Mvv5r;6q~50D9Qqo2aDw}q%!0(1Ov&EjfKmZ z8CfQ86qcI&OQ3D)C~jz+(5z=Wa`Gk Z@640=WjsN4Ffc*v137_Vb3D%+W&m+p8W#Wn diff --git a/.gitignore b/.gitignore index 229bded..ac36cd2 100644 --- a/.gitignore +++ b/.gitignore @@ -3,3 +3,4 @@ tutorials/.DS_Store problemSets/example/.Rhistory problemSets/.DS_Store .DS_Store +.Rproj.user diff --git a/problemSets/.DS_Store b/problemSets/.DS_Store index 75e9f2fbde1337e8fb5c9e913a95bf379a5659e1..d64c21c2258341956634e79a19e8c7a98c34bebc 100644 GIT binary patch literal 8196 zcmeHMPjAym6o1nO>QJCAv{29@EOJ4jf;K4ygb-=S3JQl-xMJIdZg8AwYU<2Hw%fpV zE9DFlAAk?Q2jIk!1Beq>4qWyN?12;4-8X*{x=AXKkYLrFk!F6+^WK}u`*~*U=KugH ztXC!h#sI*=D$pLprbiKaQM*c??ioTP=np_4f*49rg!wLO(_t7e3>XFs1BL;^z<+@O zd}fPc?eN@JTGJW^39cu^BS89r7Mo9 zvInAFiB2(ya!0)*%n|b%n+laX5akX;&rEcNLgeh|=SXuPd4;Am3>XHw84$VqKJb8H z-rm@rzt4u;FNeI0dfZav6yn*xWs!sQ^eH#uy7qZlu7^RKOia8def_CDdk3rmYtUMD zS9!xtyktEtc+p*PwZM5;ZpmKxPCy$ad*m8ti5D;$Nr#|9(d6DQ0juyvfv>YlEPY+2 zu+mn#WRGob=B6jdo$RHlt#N1bQg&k8naWLXZKbWz%(=_AOKV|`@yGJl1JTC_98lNo z_6bToV+;HZ9UFPqitSI^Zbg^gH@N@6!6AG2(Ba{c;nC62BS*)M9Y6k4$v#~6{IzN% ze)TmT@~9B5)5XB&%ng30iwS+02%%&j>ae>_E5Cj2T6k1Pn~~2Qa;)nSrR;7s3Mz9e zD=|$Lx5-N-dnooJ9)|Ng4w8VgrF$_FKAX_mEL-6?;|7vFR~M@I4vk{OE}z9EFN!=? zrG-b!p;xBi94qi7;Wc3?M#DhnBPvFcbGvoV4_GyG^`oLRlb>%1rb@Oky5eqr1;+!JJ0o=q7aYNUj4k6HgZ(}H+#rAF7Vf~{waQ4FaaVK}- z;x}&Kj;J~qO5w*z7bak`gPRu}+_dd}G%LAW7Fo&WzLAx7Jmx6dy+>L5CU-1)T-#lx zU-gWM{Qu{jzyEjnnGVB%VPN+#KvG4wDBcWO??|1Y^Y1g+L&{4J2Ga25c<+&ODi4#!>+!3^W2{5{PC2(LfH! 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+1,512 @@ +x = "Region", +y = "Y") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("black", "red"), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Education and Income", +x = "Monthly Net Income (Euro)", +y = "Years of University Education", +color = "Residence") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("black", "red", "green", "pink"), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Education and Income", +x = "Monthly Net Income (Euro)", +y = "Years of University Education", +color = "Residence") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("blue", "red", "green", "pink"), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("blue", "red", "green", "orange"), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("lightblue", "red", "green", "black"), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("lightblue", "red", "green", "black"), labels = c("1", "2", "3", "4")) + +scale_shape_manual(values = c(1, 4, 16, 17), labels = c("1", "2", "3", "4")) +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("lightblue", "red", "green", "black"), labels = c("1", "2", "3", "4")) + +scale_shape_manual(values = c(1, 4, 16, 17), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("lightblue", "red", "green", "black"), labels = c("1", "2", "3", "4")) + +scale_shape_manual(values = c(15, 16, 17, 18), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("lightblue", "red", "green", "black"), labels = c("1", "2", "3", "4")) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region)), shape = factor(Region)) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region)), shape = factor(Region)) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region)), shape = factor(Region))) + +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region), shape = factor(Region)) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region), shape = factor(Region)) + +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region), shape = factor(Region)) + +geom_point(size = 3) + +scale_color_manual(values = c("lightblue", "red", "green", "black"), labels = c("1", "2", "3", "4")) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region), shape = factor(Region)) + +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region), shape = factor(Region)) + +geom_point(size = 3) + +scale_color_manual(values = c("lightblue", "red", "green", "black"), labels = c("1", "2", "3", "4")) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region", +shape = "Region") +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region), shape = factor(Region)) + +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region), shape = factor(Region)) + +geom_point(size = 3) + +scale_color_manual(values = c("lightblue", "red", "green", "black"), labels = c("1", "2", "3", "4")) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region", +shape = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region") +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +lapply(c("ggplot2"), pkgTest) +expenditure <- read.table("https://raw.githubusercontent.com/ASDS-TCD/StatsI_2025/main/datasets/expenditure.txt", header=T) +head(expenditure) +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region") +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region") +ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region") +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y") +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + +geom_boxplot() + +theme( +legend.position="none", +plot.title = element_text(size=11)) + +labs(title = "Boxplot for Y for each region", +x = "Region", +y = "Y") + +theme_minimal() +ggplot(expenditure, aes(x = X2, y = X3)) + +geom_point() + +labs(title = "Relationship between X2 and X3", +x = "X2 variable", +y = "X3 variable") + +theme_minimal() +ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + +geom_boxplot() + +theme( +legend.position="none", +plot.title = element_text(size=11)) + +labs(title = "Boxplot for Y for each region", +x = "Region", +y = "Y") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +geom_point(size = 3) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y" +) +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region)) + +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region)) + +geom_point(size = 3) + +scale_color_manual(values = c("blue", "red", "green", "purple"), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region") +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region)) + +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region)) + +geom_point(size = 3) + +scale_color_manual(values = c("blue", "red", "green", "purple"), labels = c("1", "2", "3", "4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +color = "Region")) +ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + +geom_boxplot() + +theme( +legend.position="none", +plot.title = element_text(size=11)) + +labs(title = "Boxplot for Y for each region", +x = "Region", +y = "Y") + +theme_minimal() +ggplot(expenditure, aes(x = X2, y = X3)) + +geom_point() + +labs(title = "Relationship between X2 and X3", +x = "X2 variable", +y = "X3 variable") + +theme_minimal() +ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + +geom_boxplot() + +theme( +legend.position="none", +plot.title = element_text(size=11)) + +labs(title = "Boxplot for Y for each region", +x = "Region", +y = "Y") + +theme_minimal() +ggplot(df, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Education and Income", +x = "Monthly Net Income (Euro)", +y = "Years of University Education", +color = "Residence") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Education and Income", +x = "Monthly Net Income (Euro)", +y = "Years of University Education", +color = "Residence") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point() + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Education and Income", +x = "Monthly Net Income (Euro)", +y = "Years of University Education", +shape = "Region", +color = "Residence") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Education and Income", +x = "Monthly Net Income (Euro)", +y = "Years of University Education", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Education and Income", +x = "Monthly Net Income (Euro)", +y = "Years of University Education", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(21, 22, 23, 24), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(16, 22, 23, 24), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(16, 17, 18, 19), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(14, 17, 18, 19), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(11, 17, 18, 19), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(12, 17, 18, 19), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(20, 17, 18, 19), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(21, 17, 18, 19), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ts = (mean - 100)/sterror +ts +ggplot(expenditure, aes(x = X1, y = Y)) + +geom_point() + +labs(title = "Relationship between X1 and Y", +x = "X1 variable", +y = "Y variable") + +theme_minimal() +lowerlimit = mean - t * sterror +upperlimit = mean + t * sterror +lowerlimit +upperlimit +ggplot(expenditure, aes(x = X1, y = Y)) + +geom_point() + +geom_smooth(method = "lm") + +labs(title = "Relationship between X1 and Y", +x = "X1 variable", +y = "Y variable") + +theme_minimal() +ggplot(expenditure, aes(x = X2, y = Y)) + +geom_point() + +geom_smooth(method = "lm") + +labs(title = "Relationship between X2 and Y", +x = "X2 variable", +y = "Y variable") + +theme_minimal() +ggplot(expenditure, aes(x = X3, y = Y)) + +geom_point() + +geom_smooth(method = "lm") + +labs(title = "Relationship between X3 and Y", +x = "X3 variable", +y = "Y variable") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = X2)) + +geom_point() + +geom_smooth(method = "lm") +labs(title = "Relationship between X1 and X2", +x = "X1 variable", +y = "X2 variable") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = X2)) + +geom_point() + +geom_smooth(method = "lm") + +labs(title = "Relationship between X1 and X2", +x = "X1 variable", +y = "X2 variable") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = X3)) + +geom_point() + +geom_smooth(method = "lm") + +labs(title = "Relationship between X1 and X3", +x = "X1 variable", +y = "X3 variable") + +theme_minimal() +ggplot(expenditure, aes(x = X2, y = X3)) + +geom_point() + +geom_smooth(method = "lm") + +labs(title = "Relationship between X2 and X3", +x = "X2 variable", +y = "X3 variable") + +theme_minimal() +ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + +geom_boxplot() + +geom_smooth(method = "lm") + +theme( +legend.position="none", +plot.title = element_text(size=11)) + +labs(title = "Boxplot for Y for each region", +x = "Region", +y = "Y") + +theme_minimal() +ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + +geom_boxplot() + +theme( +legend.position="none", +plot.title = element_text(size=11)) + +labs(title = "Boxplot for Y for each region", +x = "Region", +y = "Y") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +geom_smooth(method = "lm") + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(21, 17, 18, 19), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + +geom_point(size = 3) + +scale_color_manual(values = c("black", "red", "green", "purple"), labels = c("region 1", "region 2", "region 3", "region 4")) + +scale_shape_manual(values = c(21, 17, 18, 19), labels = c("region 1", "region 2", "region 3", "region 4")) + +labs(title = "Relationship between Y and X1", +x = "X1", +y = "Y", +shape = "Region", +color = "Region") + +theme_minimal() +ts = (mean - 100)/sterror +ts +t = qt(p = 0.1/2, df = 24, lower.tail = F) +t +ts = (mean - 100)/sterror +ts +ts = (mean - 100)/sterror +ts +p = pt(abs(ts), df = 24, lower.tail = F) +p +p = pt(abs(ts), df = 24, lower.tail = T) +p +p = pt(abs(ts), df = 24, lower.tail = FALSE) +p diff --git a/problemSets/PS01/template/PS01.R b/problemSets/PS01/template/PS01.R index 180e69e..c8cb9f6 100644 --- a/problemSets/PS01/template/PS01.R +++ b/problemSets/PS01/template/PS01.R @@ -27,7 +27,7 @@ pkgTest <- function(pkg){ # ex: stringr # lapply(c("stringr"), pkgTest) -lapply(c(), pkgTest) +lapply(c(), pkgTest, "ggplot2") ##################### # Problem 1 @@ -35,8 +35,131 @@ lapply(c(), pkgTest) y <- c(105, 69, 86, 100, 82, 111, 104, 110, 87, 108, 87, 90, 94, 113, 112, 98, 80, 97, 95, 111, 114, 89, 95, 126, 98) +# calculate the mean +mean_y = mean(y) +mean_y + +# calculate the standard deviation +stdev = sd(y) +stdev +#demeanedSum <- y - mean +#sum(demeanedSum) +#squaredError <- demeanedSum ^ 2 +#sum(squaredError) +#variance <- sum(squaredError)/(length(y)-1) +#variance +#stdev = sqrt(variance) +#stdev + +# calculate the standard error +sterror = stdev/sqrt(length(y)) +sterror + +# find the t-score for the desired confidence level +p = (1 - 0.9)/2 +p +t = qt(p = p, df = 24, lower.tail = FALSE) +t + +# construct the confidence interval +lowerlimit = mean_y - t * sterror +upperlimit = mean_y + t * sterror +lowerlimit +upperlimit + +# hypothesis testing +# step 1 - assumptions: data is quantitative, sampling method is random, sample size is smaller than 30 -> t-score instead of z-score + +# step 2- null hypothesis: mean is lower or equal to 100 +# alternative hypothesis: mean is higher than 100 + +# step 3 - calculate a test statistic +ts = (mean_y - 100)/sterror +ts + +# step 4 - calculate the p-value +p = pt(ts, df = 24, lower.tail = FALSE) +p +# step 5 - conclusion +# p-value is higher than alpha -> cannot reject the null hypothesis that the mean is lower or equal to 100 + + ##################### # Problem 2 ##################### +lapply(c("ggplot2"), pkgTest) expenditure <- read.table("https://raw.githubusercontent.com/ASDS-TCD/StatsI_2025/main/datasets/expenditure.txt", header=T) +head(expenditure) + +ggplot(expenditure, aes(x = X1, y = Y)) + + geom_point() + + labs(title = "Relationship between personal income and housing assistance expenditure", + x = "personal income (USD per capita)", + y = "expenditure on housing assistance (USD per capita)") + + theme_minimal() + +ggplot(expenditure, aes(x = X2, y = Y)) + + geom_point() + + labs(title = "Relationship between financial insecurity and housing assistance expenditure", + x = "number of financially insecure residents (per 100,000)", + y = "expenditure on housing assistance (USD per capita)") + + theme_minimal() + +ggplot(expenditure, aes(x = X3, y = Y)) + + geom_point() + + labs(title = "Relationship between urban residency and expenditure on housing assistance (in state)", + x = "number of urban residents (per 1000)", + y = "expenditure on housing assistance (USD per capita)") + + theme_minimal() + +ggplot(expenditure, aes(x = X1, y = X2)) + + geom_point() + + #geom_smooth(method = "lm") + + labs(title = "Relationship between personal income and financial insecurity", + x = "personal income (USD per capita)", + y = "number of financially insecure residents (per 100,000)")+ + theme_minimal() + +ggplot(expenditure, aes(x = X1, y = X3)) + + geom_point() + + labs(title = "Relationship between personal income and urban residency", + x = "personal income (USD per capita)", + y = "number of urban residents (per 1000)") + + theme_minimal() + +ggplot(expenditure, aes(x = X2, y = X3)) + + geom_point() + + labs(title = "Relationship between financial insecurity and urban residency", + x = "number of financially insecure residents (per 100,000)", + y = "number of urban residents (per 1000)") + + theme_minimal() + +expenditure$Region <- factor(expenditure$Region, + levels = c(1, 2, 3, 4), + labels = c("Northeast", "North Central", "South", "West")) + +ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + + geom_boxplot() + + theme( + legend.position="none", + plot.title = element_text(size=11)) + + labs(title = "Boxplot for housing assistance expenditure for each region", + x = "Region", + y = "expenditure on housing assistance (USD per capita)") + + theme_minimal() + +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + + geom_point(size = 3) + + scale_color_manual(values = c("black", "red", "green", "purple")) + + scale_shape_manual(values = c(21, 17, 18, 19)) + + labs(title = "Relationship between personal income and house assistance expenditure per region", + x = "personal income (USD per capita)", + y = "expenditure on housing assistance (USD per capita)", + shape = "Region", + color = "Region") + + theme_minimal() + + + + diff --git a/problemSets/PS01/template/PS01.log b/problemSets/PS01/template/PS01.log new file mode 100644 index 0000000..fc8cc71 --- /dev/null +++ b/problemSets/PS01/template/PS01.log @@ 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LaTeX Error: File `setspace.sty' not found. + +Type X to quit or to proceed, +or enter new name. (Default extension: sty) + +Enter file name: +! Emergency stop. + + +l.5 \usepackage + {fullpage}^^M +*** (cannot \read from terminal in nonstop modes) + + +Here is how much of TeX's memory you used: + 1067 strings out of 469781 + 14820 string characters out of 5481415 + 427298 words of memory out of 5000000 + 29515 multiletter control sequences out of 15000+600000 + 627123 words of font info for 41 fonts, out of 8000000 for 9000 + 14 hyphenation exceptions out of 8191 + 57i,0n,65p,200b,36s stack positions out of 10000i,1000n,20000p,200000b,200000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/problemSets/PS01/template/PS01.tex b/problemSets/PS01/template/PS01.tex index 60db0e2..2bfffda 100644 --- a/problemSets/PS01/template/PS01.tex +++ b/problemSets/PS01/template/PS01.tex @@ -1,4 +1,4 @@ -\documentclass[12pt,letterpaper]{article} +\documentclass[12pt,letterpaper]{article}[[[[[[[[[[[;]]]]]]]]]]] \usepackage{graphicx,textcomp} \usepackage{natbib} \usepackage{setspace} diff --git a/problemSets/PS01/template/template.Rproj b/problemSets/PS01/template/template.Rproj new file mode 100644 index 0000000..8e3c2eb --- /dev/null +++ b/problemSets/PS01/template/template.Rproj @@ -0,0 +1,13 @@ +Version: 1.0 + +RestoreWorkspace: Default +SaveWorkspace: Default +AlwaysSaveHistory: Default + +EnableCodeIndexing: Yes +UseSpacesForTab: Yes +NumSpacesForTab: 2 +Encoding: UTF-8 + +RnwWeave: Sweave +LaTeX: pdfLaTeX diff --git a/problemSets/answers_DP/PS01_DP.R b/problemSets/answers_DP/PS01_DP.R new file mode 100644 index 0000000..c8cb9f6 --- /dev/null +++ b/problemSets/answers_DP/PS01_DP.R @@ -0,0 +1,165 @@ +##################### +# load libraries +# set wd +# clear global .envir +##################### + +# remove objects +rm(list=ls()) +# detach all libraries +detachAllPackages <- function() { + basic.packages <- c("package:stats", "package:graphics", "package:grDevices", "package:utils", "package:datasets", "package:methods", "package:base") + package.list <- search()[ifelse(unlist(gregexpr("package:", search()))==1, TRUE, FALSE)] + package.list <- setdiff(package.list, basic.packages) + if (length(package.list)>0) for (package in package.list) detach(package, character.only=TRUE) +} +detachAllPackages() + +# load libraries +pkgTest <- function(pkg){ + new.pkg <- pkg[!(pkg %in% installed.packages()[, "Package"])] + if (length(new.pkg)) + install.packages(new.pkg, dependencies = TRUE) + sapply(pkg, require, character.only = TRUE) +} + +# here is where you load any necessary packages +# ex: stringr +# lapply(c("stringr"), pkgTest) + +lapply(c(), pkgTest, "ggplot2") + +##################### +# Problem 1 +##################### + +y <- c(105, 69, 86, 100, 82, 111, 104, 110, 87, 108, 87, 90, 94, 113, 112, 98, 80, 97, 95, 111, 114, 89, 95, 126, 98) + +# calculate the mean +mean_y = mean(y) +mean_y + +# calculate the standard deviation +stdev = sd(y) +stdev +#demeanedSum <- y - mean +#sum(demeanedSum) +#squaredError <- demeanedSum ^ 2 +#sum(squaredError) +#variance <- sum(squaredError)/(length(y)-1) +#variance +#stdev = sqrt(variance) +#stdev + +# calculate the standard error +sterror = stdev/sqrt(length(y)) +sterror + +# find the t-score for the desired confidence level +p = (1 - 0.9)/2 +p +t = qt(p = p, df = 24, lower.tail = FALSE) +t + +# construct the confidence interval +lowerlimit = mean_y - t * sterror +upperlimit = mean_y + t * sterror +lowerlimit +upperlimit + +# hypothesis testing +# step 1 - assumptions: data is quantitative, sampling method is random, sample size is smaller than 30 -> t-score instead of z-score + +# step 2- null hypothesis: mean is lower or equal to 100 +# alternative hypothesis: mean is higher than 100 + +# step 3 - calculate a test statistic +ts = (mean_y - 100)/sterror +ts + +# step 4 - calculate the p-value +p = pt(ts, df = 24, lower.tail = FALSE) +p +# step 5 - conclusion +# p-value is higher than alpha -> cannot reject the null hypothesis that the mean is lower or equal to 100 + + +##################### +# Problem 2 +##################### +lapply(c("ggplot2"), pkgTest) + +expenditure <- read.table("https://raw.githubusercontent.com/ASDS-TCD/StatsI_2025/main/datasets/expenditure.txt", header=T) +head(expenditure) + +ggplot(expenditure, aes(x = X1, y = Y)) + + geom_point() + + labs(title = "Relationship between personal income and housing assistance expenditure", + x = "personal income (USD per capita)", + y = "expenditure on housing assistance (USD per capita)") + + theme_minimal() + +ggplot(expenditure, aes(x = X2, y = Y)) + + geom_point() + + labs(title = "Relationship between financial insecurity and housing assistance expenditure", + x = "number of financially insecure residents (per 100,000)", + y = "expenditure on housing assistance (USD per capita)") + + theme_minimal() + +ggplot(expenditure, aes(x = X3, y = Y)) + + geom_point() + + labs(title = "Relationship between urban residency and expenditure on housing assistance (in state)", + x = "number of urban residents (per 1000)", + y = "expenditure on housing assistance (USD per capita)") + + theme_minimal() + +ggplot(expenditure, aes(x = X1, y = X2)) + + geom_point() + + #geom_smooth(method = "lm") + + labs(title = "Relationship between personal income and financial insecurity", + x = "personal income (USD per capita)", + y = "number of financially insecure residents (per 100,000)")+ + theme_minimal() + +ggplot(expenditure, aes(x = X1, y = X3)) + + geom_point() + + labs(title = "Relationship between personal income and urban residency", + x = "personal income (USD per capita)", + y = "number of urban residents (per 1000)") + + theme_minimal() + +ggplot(expenditure, aes(x = X2, y = X3)) + + geom_point() + + labs(title = "Relationship between financial insecurity and urban residency", + x = "number of financially insecure residents (per 100,000)", + y = "number of urban residents (per 1000)") + + theme_minimal() + +expenditure$Region <- factor(expenditure$Region, + levels = c(1, 2, 3, 4), + labels = c("Northeast", "North Central", "South", "West")) + +ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + + geom_boxplot() + + theme( + legend.position="none", + plot.title = element_text(size=11)) + + labs(title = "Boxplot for housing assistance expenditure for each region", + x = "Region", + y = "expenditure on housing assistance (USD per capita)") + + theme_minimal() + +ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + + geom_point(size = 3) + + scale_color_manual(values = c("black", "red", "green", "purple")) + + scale_shape_manual(values = c(21, 17, 18, 19)) + + labs(title = "Relationship between personal income and house assistance expenditure per region", + x = "personal income (USD per capita)", + y = "expenditure on housing assistance (USD per capita)", + shape = "Region", + color = "Region") + + theme_minimal() + + + + diff --git a/problemSets/answers_DP/PS01_DP.aux b/problemSets/answers_DP/PS01_DP.aux new file mode 100644 index 0000000..e69de29 diff --git a/problemSets/answers_DP/PS01_DP.tex b/problemSets/answers_DP/PS01_DP.tex new file mode 100644 index 0000000..cc76651 --- /dev/null +++ b/problemSets/answers_DP/PS01_DP.tex @@ -0,0 +1,130 @@ +\documentclass[12pt,letterpaper]{article} +\usepackage{graphicx,textcomp} +\usepackage{natbib} +\usepackage{setspace} +\usepackage[a4paper,margin=1in]{geometry} +\usepackage{color} +\usepackage[reqno]{amsmath} +\usepackage{amsthm} +\usepackage{fancyvrb} +\usepackage{amssymb,enumerate} +\usepackage[all]{xy} +\usepackage{endnotes} +\usepackage{lscape} +\newtheorem{com}{Comment} +\usepackage{float} +\usepackage{hyperref} +\newtheorem{lem} {Lemma} +\newtheorem{prop}{Proposition} +\newtheorem{thm}{Theorem} +\newtheorem{defn}{Definition} +\newtheorem{cor}{Corollary} +\newtheorem{obs}{Observation} +\usepackage[compact]{titlesec} +\usepackage{dcolumn} +\usepackage{tikz} +\usetikzlibrary{arrows} +\usepackage{multirow} +\usepackage{xcolor} +\newcolumntype{.}{D{.}{.}{-1}} +\newcolumntype{d}[1]{D{.}{.}{#1}} +\definecolor{light-gray}{gray}{0.65} +\usepackage{url} +\usepackage{listings} +\usepackage{color} + +\definecolor{codegreen}{rgb}{0,0.6,0} +\definecolor{codegray}{rgb}{0.5,0.5,0.5} +\definecolor{codepurple}{rgb}{0.58,0,0.82} +\definecolor{backcolour}{rgb}{0.95,0.95,0.92} + +\lstdefinestyle{mystyle}{ + backgroundcolor=\color{backcolour}, + commentstyle=\color{codegreen}, + keywordstyle=\color{magenta}, + numberstyle=\tiny\color{codegray}, + stringstyle=\color{codepurple}, + basicstyle=\footnotesize, + breakatwhitespace=false, + breaklines=true, + captionpos=b, + keepspaces=true, + numbers=left, + numbersep=5pt, + showspaces=false, + showstringspaces=false, + showtabs=false, + tabsize=2 +} +\lstset{style=mystyle} +\newcommand{\Sref}[1]{Section~\ref{#1}} +\newtheorem{hyp}{Hypothesis} + +\title{Problem Set 1} +\date{Due: October 9, 2025} +\author{Applied Stats/Quant Methods 1} + +\begin{document} + \maketitle + + \section*{Instructions} + \begin{itemize} + \item Please show your work! You may lose points by simply writing in the answer. If the problem requires you to execute commands in \texttt{R}, please include the code you used to get your answers. Please also include the \texttt{.R} file that contains your code. If you are not sure if work needs to be shown for a particular problem, please ask. +\item Your homework should be submitted electronically on GitHub. +\item This problem set is due before 23:59 on Thursday October 9, 2025. No late assignments will be accepted. + \end{itemize} + + \vspace{1cm} + \section*{Question 1: Education} + +A school counselor was curious about the average of IQ of the students in her school and took a random sample of 25 students' IQ scores. The following is the data set:\\ +\vspace{.5cm} + +\lstinputlisting[language=R, firstline=36, lastline=36]{PS01_DP.R} + +\vspace{1cm} + +\begin{enumerate} + \item Find a 90\% confidence interval for the average student IQ in the school.\\ + + \item Next, the school counselor was curious whether the average student IQ in her school is higher than the average IQ score (100) among all the schools in the country.\\ + + \noindent Using the same sample, conduct the appropriate hypothesis test with $\alpha=0.05$. +\end{enumerate} + +\newpage + + \section*{Question 2: Political Economy} + +\noindent Researchers are curious about what affects the amount of money communities spend on addressing homelessness. The following variables constitute our data set about social welfare expenditures in the USA. \\ +\vspace{.5cm} + + +\begin{tabular}{r|l} + \texttt{State} &\emph{50 states in US} \\ + \texttt{Y} & \emph{per capita expenditure on shelters/housing assistance in state}\\ + \texttt{X1} &\emph{per capita personal income in state} \\ + \texttt{X2} & \emph{Number of residents per 100,000 that are "financially insecure" in state}\\ + \texttt{X3} & \emph{Number of people per thousand residing in urban areas in state} \\ + \texttt{Region} & \emph{1=Northeast, 2= North Central, 3= South, 4=West} \\ +\end{tabular} + +\vspace{.5cm} +\noindent Explore the \texttt{expenditure} data set and import data into \texttt{R}. +\vspace{.5cm} +\lstinputlisting[language=R, firstline=54, lastline=54]{PS01.R} +\vspace{.5cm} +\begin{itemize} + +\item +Please plot the relationships among \emph{Y}, \emph{X1}, \emph{X2}, and \emph{X3}? What are the correlations among them (you just need to describe the graph and the relationships among them)? +\vspace{.5cm} +\item +Please plot the relationship between \emph{Y} and \emph{Region}? On average, which region has the highest per capita expenditure on housing assistance? +\vspace{.5cm} +\item +Please plot the relationship between \emph{Y} and \emph{X1}? Describe this graph and the relationship. Reproduce the above graph including one more variable \emph{Region} and display different regions with different types of symbols and colors. +\end{itemize} + + +\end{document} From d8dd0d96d9b51ae2f0765720d4564c249e59b22b Mon Sep 17 00:00:00 2001 From: Damaris Parasca <126685870+damarisparasca@users.noreply.github.com> Date: Wed, 8 Oct 2025 12:50:58 +0100 Subject: [PATCH 5/9] update --- problemSets/.DS_Store | Bin 8196 -> 8196 bytes problemSets/answers_DP/.Rapp.history | 0 problemSets/answers_DP/PS01_DP.aux | 7 + problemSets/answers_DP/PS01_DP.log | 755 ++++++++++++++++++++++ problemSets/answers_DP/PS01_DP.out | 0 problemSets/answers_DP/PS01_DP.pdf | Bin 0 -> 112064 bytes problemSets/answers_DP/PS01_DP.synctex.gz | Bin 0 -> 17312 bytes problemSets/answers_DP/PS01_DP.tex | 5 +- 8 files changed, 765 insertions(+), 2 deletions(-) create mode 100644 problemSets/answers_DP/.Rapp.history create mode 100644 problemSets/answers_DP/PS01_DP.log create mode 100644 problemSets/answers_DP/PS01_DP.out create mode 100644 problemSets/answers_DP/PS01_DP.pdf create mode 100644 problemSets/answers_DP/PS01_DP.synctex.gz diff --git a/problemSets/.DS_Store b/problemSets/.DS_Store index d64c21c2258341956634e79a19e8c7a98c34bebc..f08944950ec2effb4693576c761e586d56a5b623 100644 GIT binary patch delta 16 XcmZp1XmQwZQ(*E2QMb+Vf=~GXJEI1c delta 24 fcmZp1XmQwZQ-IyfP)EVY(q!^N5&O;Zf=~GXWt#`s diff --git a/problemSets/answers_DP/.Rapp.history b/problemSets/answers_DP/.Rapp.history new file mode 100644 index 0000000..e69de29 diff --git a/problemSets/answers_DP/PS01_DP.aux b/problemSets/answers_DP/PS01_DP.aux index e69de29..f2a0ba9 100644 --- a/problemSets/answers_DP/PS01_DP.aux +++ b/problemSets/answers_DP/PS01_DP.aux @@ -0,0 +1,7 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\@writefile{lol}{\contentsline {lstlisting}{PS01\textunderscore DP.R}{1}{lstlisting.-1}\protected@file@percent } +\@writefile{lol}{\contentsline {lstlisting}{PS01\textunderscore DP.R}{2}{lstlisting.-2}\protected@file@percent } +\gdef \@abspage@last{2} diff --git a/problemSets/answers_DP/PS01_DP.log b/problemSets/answers_DP/PS01_DP.log new file mode 100644 index 0000000..40a3267 --- /dev/null +++ b/problemSets/answers_DP/PS01_DP.log @@ -0,0 +1,755 @@ +This is pdfTeX, Version 3.141592653-2.6-1.40.28 (TeX Live 2025) (preloaded format=pdflatex 2025.10.7) 7 OCT 2025 20:33 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**PS01_DP.tex +(./PS01_DP.tex +LaTeX2e <2025-06-01> patch level 1 +L3 programming layer <2025-08-13> +(/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/base/article.cls +Document Class: article 2025/01/22 v1.4n Standard LaTeX document class +(/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/base/size12.clo +File: size12.clo 2025/01/22 v1.4n Standard LaTeX file (size option) +) +\c@part=\count275 +\c@section=\count276 +\c@subsection=\count277 +\c@subsubsection=\count278 +\c@paragraph=\count279 +\c@subparagraph=\count280 +\c@figure=\count281 +\c@table=\count282 +\abovecaptionskip=\skip49 +\belowcaptionskip=\skip50 +\bibindent=\dimen148 +) (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/graphics/graphicx.sty +Package: graphicx 2024/12/31 v1.2e Enhanced LaTeX Graphics (DPC,SPQR) + (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/graphics/keyval.sty +Package: keyval 2022/05/29 v1.15 key=value parser (DPC) +\KV@toks@=\toks17 +) (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/graphics/graphics.sty +Package: graphics 2024/08/06 v1.4g Standard LaTeX Graphics (DPC,SPQR) + (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/graphics/trig.sty +Package: trig 2023/12/02 v1.11 sin cos tan (DPC) +) (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/graphics-cfg/graphics.cfg +File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration +) +Package graphics Info: Driver file: pdftex.def on input line 106. + (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/graphics-def/pdftex.def +File: pdftex.def 2024/04/13 v1.2c Graphics/color driver for pdftex +)) +\Gin@req@height=\dimen149 +\Gin@req@width=\dimen150 +) (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/base/textcomp.sty +Package: textcomp 2024/04/24 v2.1b Standard LaTeX package +) (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/natbib/natbib.sty +Package: natbib 2010/09/13 8.31b (PWD, AO) +\bibhang=\skip51 +\bibsep=\skip52 +LaTeX Info: Redefining \cite on input line 694. +\c@NAT@ctr=\count283 +) (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/setspace/setspace.sty +Package: setspace 2022/12/04 v6.7b set line spacing +) (/Users/damirish/Library/TinyTeX/texmf-dist/tex/latex/geometry/geometry.sty +Package: geometry 2020/01/02 v5.9 Page Geometry + (/Users/damirish/Library/TinyTeX/texmf-dist/tex/generic/iftex/ifvtex.sty +Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. 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tt9xMIzxkKP?+-6LYh&O1$%HBApPsLuZoj>JzkmPc{{d`eux>b10RT|(uZ#cy literal 0 HcmV?d00001 diff --git a/problemSets/answers_DP/PS01_DP.tex b/problemSets/answers_DP/PS01_DP.tex index cc76651..6433cc3 100644 --- a/problemSets/answers_DP/PS01_DP.tex +++ b/problemSets/answers_DP/PS01_DP.tex @@ -112,7 +112,7 @@ \vspace{.5cm} \noindent Explore the \texttt{expenditure} data set and import data into \texttt{R}. \vspace{.5cm} -\lstinputlisting[language=R, firstline=54, lastline=54]{PS01.R} +\lstinputlisting[language=R, firstline=54, lastline=60]{PS01_DP.R} \vspace{.5cm} \begin{itemize} @@ -126,5 +126,6 @@ Please plot the relationship between \emph{Y} and \emph{X1}? Describe this graph and the relationship. Reproduce the above graph including one more variable \emph{Region} and display different regions with different types of symbols and colors. \end{itemize} - + \section*{Solution - Question 2: Political Economy} \end{document} + From 06f6812965937706caed75aaeb0c91335a1f14fb Mon Sep 17 00:00:00 2001 From: Damaris Parasca <126685870+damarisparasca@users.noreply.github.com> Date: Wed, 8 Oct 2025 12:56:47 +0100 Subject: [PATCH 6/9] update --- problemSets/answers_DP/PS01_DP.log | 2 +- problemSets/answers_DP/PS01_DP.pdf | Bin 112064 -> 112064 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/problemSets/answers_DP/PS01_DP.log b/problemSets/answers_DP/PS01_DP.log index 40a3267..725d7dc 100644 --- a/problemSets/answers_DP/PS01_DP.log +++ b/problemSets/answers_DP/PS01_DP.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.28 (TeX Live 2025) (preloaded format=pdflatex 2025.10.7) 7 OCT 2025 20:33 +This is pdfTeX, Version 3.141592653-2.6-1.40.28 (TeX Live 2025) (preloaded format=pdflatex 2025.10.7) 8 OCT 2025 12:56 entering extended mode restricted \write18 enabled. %&-line parsing enabled. diff --git a/problemSets/answers_DP/PS01_DP.pdf b/problemSets/answers_DP/PS01_DP.pdf index 21af95b4f900e51b1bb8f7cc814ea34271b322f4..e978eb295f1f795e95508ce8e0c94ae25dac40ba 100644 GIT binary patch delta 112 zcmX@`n(e@AwuUW?!OPh#42?|949%uTEoYR0akkekXI#ePY;0ocXzplkXk=+&Xl~$S gYHa3gX=-F-;9_LtWZ-6IX{TUANXhoJEsRl&03jP4p8x;= delta 112 zcmX@`n(e@AwuUW?!OPjrjSP&94NRs-EoYR0akkekXI#eP>}Fu>?C5OZ=w{($?rP*} gX<}k*XyRz;XlZ8VY-r|cWT#+5NXhoJEsRl&06o1PPXGV_ From ba838c06e6273cf1e06d4adcca5d88341828d087 Mon Sep 17 00:00:00 2001 From: Damaris Parasca <126685870+damarisparasca@users.noreply.github.com> Date: Wed, 8 Oct 2025 13:59:54 +0100 Subject: [PATCH 7/9] created my_answers --- .DS_Store | Bin 6148 -> 8196 bytes problemSets/.DS_Store | Bin 8196 -> 8196 bytes .../my_answers}/.Rapp.history | 0 .../{answers_DP => PS01/my_answers}/PS01_DP.R | 0 .../my_answers}/PS01_DP.aux | 4 ++-- .../my_answers}/PS01_DP.log | 22 +++++++++++------- .../my_answers}/PS01_DP.out | 0 .../my_answers}/PS01_DP.pdf | Bin 112064 -> 112721 bytes .../PS01/my_answers/PS01_DP.synctex.gz | Bin 0 -> 17635 bytes .../my_answers}/PS01_DP.tex | 5 ++-- problemSets/answers_DP/PS01_DP.synctex.gz | Bin 17312 -> 0 bytes 11 files changed, 18 insertions(+), 13 deletions(-) rename problemSets/{answers_DP => PS01/my_answers}/.Rapp.history (100%) rename problemSets/{answers_DP => PS01/my_answers}/PS01_DP.R (100%) rename problemSets/{answers_DP => PS01/my_answers}/PS01_DP.aux (81%) rename problemSets/{answers_DP => PS01/my_answers}/PS01_DP.log (98%) rename problemSets/{answers_DP => PS01/my_answers}/PS01_DP.out (100%) rename problemSets/{answers_DP => PS01/my_answers}/PS01_DP.pdf (78%) create mode 100644 problemSets/PS01/my_answers/PS01_DP.synctex.gz rename problemSets/{answers_DP => PS01/my_answers}/PS01_DP.tex (98%) delete mode 100644 problemSets/answers_DP/PS01_DP.synctex.gz diff --git a/.DS_Store b/.DS_Store index feeea16b89feb316bc972d2dbaa0521111abfc90..2bf9978dd8b26d489195a7edd0a250a803013bbd 100644 GIT binary patch literal 8196 zcmeHM&u`N(6n-v)rHnx~HYf@ zXOK8>7w2UFK(f`+I6w*j z46FjpK5RM^F)nIbNvNJfhy?inAy9}Q%=z4H^VS_&0j+>mKr5gX&E}Hs)yGvU=BJC0@(&Dl3ICH!lZ_ zq>(I|sjaQa3*#f!#Ko!Y5o_z>#Mp>6HF;rsJ82B3&tF<7KK3^le~vrBLezr}`sMGP z_61sdXyUn>YIo#gV|QOnv$4PA!M;QNhmV*8gGUF328M@+j~!2)IC=6^(LCzd?&ESG z{_bh+^C0V2X~A9QPB|oj^Q$RvA_PFGm`GEPHmC-}6ldyncbrojdHsUCTOX=6}N{Dl_ zIhd0ewpFYggUrK6fZrOviQxB)E(xm+TIi7K-jM2Wxm&^s@BA(<`{dqIBLAPoV_km- z=;Dj5x26@?Ljlq=lb;bU`HlCFRzLC1U}1fTRTSY@ml#v95iX)XPR9{<{$Yr=rN%M} d>k@GU%isDC(CM|h!-1gBe|`SP_i48^KLP#MY-|7k delta 269 zcmZp1XfcprU|?W$DortDU=RQ@Ie-{Mvv5r;6q~50D9Q$s2a6Rmq%xE+6epDz7i=tC z&MXX);b2H%NCb)|GJs_#`-?P*7+DzWC>R=;)aocyTN)VXD43X;OzsmjmPJ#{P+S&V zl$VpAmkzRG@fDN+;2m}ZL2ea7| k*8vAMF)Sc5IW&`@6hE`}75)LUCk)^Nvj-UW1hIJr11BFAy8r+H delta 411 zcmZp1XmOa}FUrrrz`)4BAi%(o%232m%n;Au!Vs{ra2or>2Hwr=94s8ZAQfB;i41u_ z*>Yr6o;mr+NjdpRKzX2cMkOGv_a6*^EF5|!`v^2}7#kbuC>R?VPktq6FN)RZ%|=3Z z80)c0<)j-1C+FuDfbD<~Sk>j`ySPAI$Kj|aUvtFkxFarC<>segQR{`>+XWfKIiM`K qC@&{JFCAzp<7OU#>x}GBZ*P7jXv;LQRCqJH#CMj-hJu^WBm@97>Rnj? 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b/problemSets/PS01/my_answers/PS01_DP.tex @@ -93,7 +93,8 @@ \end{enumerate} \newpage - + \section*{Solution - Question 1: Education} +\newpage \section*{Question 2: Political Economy} \noindent Researchers are curious about what affects the amount of money communities spend on addressing homelessness. The following variables constitute our data set about social welfare expenditures in the USA. \\ @@ -125,7 +126,7 @@ \item Please plot the relationship between \emph{Y} and \emph{X1}? Describe this graph and the relationship. Reproduce the above graph including one more variable \emph{Region} and display different regions with different types of symbols and colors. \end{itemize} - +\newpage \section*{Solution - Question 2: Political Economy} \end{document} diff --git a/problemSets/answers_DP/PS01_DP.synctex.gz b/problemSets/answers_DP/PS01_DP.synctex.gz deleted file mode 100644 index 9b0593f94e621c81493ab2cd4bfbb73b96293357..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 17312 zcmYJZ1yCH%^9LG8AOwdXhkFR_c35zCf^!6ScQ_!p26qka?(TZHyC3fEd3=BWdhc!3 z)y`GV_H=J|f4XP3Nx~66{O|f&@1-3@%oDrT>fMi8g~sr=wf|YHl9%b@;zidfhZP`P zs8}_2B)?=@Ex}~g@}cuN{e?A77CvPof7$WyEsPJNo07t>``NZrQ0HG`+P_PMf3JIo zk9U__?cUc(!L}QE>&N%!Z?|~n=K`R$4S_WQANTwHwEfnkLECe0&t?zzH^@c=>)Tpm z;UJox?U_%jySumR?Zpck`pfBrkJtTiYv)@5yZ7sp!?mG_*{9xrPS0D1M~C;W|4#3= zT(P!@s_wJAAKji`da}+tK$lr06`8i{y8P{{AfNWf+o$8}(XkG{mFrWVRkM#KQEY6k 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39180 bytes problemSets/PS01/my_answers/PS01_DP.tex | 115 +++++++++++++++- problemSets/PS01/my_answers/boxplot_reg_y.png | Bin 0 -> 23683 bytes problemSets/PS01/my_answers/scatter_x1_x2.png | Bin 0 -> 29831 bytes problemSets/PS01/my_answers/scatter_x1_x3.png | Bin 0 -> 29698 bytes problemSets/PS01/my_answers/scatter_x1_y.pdf | Bin 0 -> 30382 bytes problemSets/PS01/my_answers/scatter_x1_y.png | Bin 0 -> 30382 bytes problemSets/PS01/my_answers/scatter_x2_x3.png | Bin 0 -> 30482 bytes problemSets/PS01/my_answers/scatter_x2_y.png | Bin 0 -> 30948 bytes problemSets/PS01/my_answers/scatter_x3_y.png | Bin 0 -> 30480 bytes problemSets/PS01/template/.Rapp.history | 0 problemSets/example/PS01_answersJZ.log | 77 +++++++++++ 16 files changed, 367 insertions(+), 36 deletions(-) create mode 100644 problemSets/PS01/my_answers/boxplot_reg_y.png create mode 100644 problemSets/PS01/my_answers/scatter_x1_x2.png create mode 100644 problemSets/PS01/my_answers/scatter_x1_x3.png create mode 100644 problemSets/PS01/my_answers/scatter_x1_y.pdf create mode 100644 problemSets/PS01/my_answers/scatter_x1_y.png create mode 100644 problemSets/PS01/my_answers/scatter_x2_x3.png create mode 100644 problemSets/PS01/my_answers/scatter_x2_y.png create mode 100644 problemSets/PS01/my_answers/scatter_x3_y.png create mode 100644 problemSets/PS01/template/.Rapp.history create mode 100644 problemSets/example/PS01_answersJZ.log diff --git a/problemSets/PS01/my_answers/PS01_DP.R b/problemSets/PS01/my_answers/PS01_DP.R index c8cb9f6..8497233 100644 --- a/problemSets/PS01/my_answers/PS01_DP.R +++ b/problemSets/PS01/my_answers/PS01_DP.R @@ -40,25 +40,18 @@ mean_y = mean(y) mean_y # calculate the standard deviation -stdev = sd(y) +demeanedSum <- y - mean_y +squaredError <- demeanedSum ^ 2 +variance <- sum(squaredError)/(length(y)-1) +stdev = sqrt(variance) stdev -#demeanedSum <- y - mean -#sum(demeanedSum) -#squaredError <- demeanedSum ^ 2 -#sum(squaredError) -#variance <- sum(squaredError)/(length(y)-1) -#variance -#stdev = sqrt(variance) -#stdev # calculate the standard error sterror = stdev/sqrt(length(y)) sterror # find the t-score for the desired confidence level -p = (1 - 0.9)/2 -p -t = qt(p = p, df = 24, lower.tail = FALSE) +t = qt(p = (1 - 0.9)/2 , df = 24, lower.tail = FALSE) t # construct the confidence interval @@ -80,6 +73,7 @@ ts # step 4 - calculate the p-value p = pt(ts, df = 24, lower.tail = FALSE) p + # step 5 - conclusion # p-value is higher than alpha -> cannot reject the null hypothesis that the mean is lower or equal to 100 @@ -88,57 +82,85 @@ p # Problem 2 ##################### lapply(c("ggplot2"), pkgTest) +install.packages("ggpubr") +library(ggpubr) expenditure <- read.table("https://raw.githubusercontent.com/ASDS-TCD/StatsI_2025/main/datasets/expenditure.txt", header=T) head(expenditure) +# plot the relationships between all the variables +# add the correlation coefficient and hide the p-value +# save the plots as a png to add to the latex file + +png(file = "scatter_x1_y.pdf") ggplot(expenditure, aes(x = X1, y = Y)) + geom_point() + labs(title = "Relationship between personal income and housing assistance expenditure", x = "personal income (USD per capita)", y = "expenditure on housing assistance (USD per capita)") + - theme_minimal() + stat_cor(aes(label = ..r.label..)) + + theme_minimal() +dev.off() +png(file = "scatter_x2_y.png") ggplot(expenditure, aes(x = X2, y = Y)) + geom_point() + labs(title = "Relationship between financial insecurity and housing assistance expenditure", x = "number of financially insecure residents (per 100,000)", y = "expenditure on housing assistance (USD per capita)") + + stat_cor(aes(label = ..r.label..)) + theme_minimal() +dev.off() +png(file = "scatter_x3_y.png") ggplot(expenditure, aes(x = X3, y = Y)) + geom_point() + labs(title = "Relationship between urban residency and expenditure on housing assistance (in state)", x = "number of urban residents (per 1000)", y = "expenditure on housing assistance (USD per capita)") + + stat_cor(aes(label = ..r.label..)) + theme_minimal() +dev.off() +png(file = "scatter_x1_x2.png") ggplot(expenditure, aes(x = X1, y = X2)) + geom_point() + - #geom_smooth(method = "lm") + labs(title = "Relationship between personal income and financial insecurity", x = "personal income (USD per capita)", y = "number of financially insecure residents (per 100,000)")+ + stat_cor(aes(label = ..r.label..)) + theme_minimal() +dev.off() +png(file = "scatter_x1_x3.png") ggplot(expenditure, aes(x = X1, y = X3)) + geom_point() + labs(title = "Relationship between personal income and urban residency", x = "personal income (USD per capita)", y = "number of urban residents (per 1000)") + + stat_cor(aes(label = ..r.label..)) + theme_minimal() +dev.off() +png(file = "scatter_x2_x3.png") ggplot(expenditure, aes(x = X2, y = X3)) + geom_point() + labs(title = "Relationship between financial insecurity and urban residency", x = "number of financially insecure residents (per 100,000)", y = "number of urban residents (per 1000)") + + stat_cor(aes(label = ..r.label..)) + theme_minimal() - +dev.off() + + +# turn the Region into a factor to make the plot more readable +# now it shows the name of the region instead of 1,2,3,4 expenditure$Region <- factor(expenditure$Region, levels = c(1, 2, 3, 4), labels = c("Northeast", "North Central", "South", "West")) +# make a boxplot to compare the per capita housing expenditure in different regions +png(file = "boxplot_reg_y.png") ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + geom_boxplot() + theme( @@ -147,18 +169,23 @@ ggplot(expenditure, aes(x=Region, y=Y, group=Region)) + labs(title = "Boxplot for housing assistance expenditure for each region", x = "Region", y = "expenditure on housing assistance (USD per capita)") + - theme_minimal() + theme_minimal() +dev.off() +# plot the relationship between x1, y and region +# each region is represented by a different shape and colour +png(file = "scatter_x1_y_reg.png") ggplot(expenditure, aes(x = X1, y = Y, shape = factor(Region), color = factor(Region))) + - geom_point(size = 3) + + geom_point(size = 3) + # increase size to distinguish between the shapes scale_color_manual(values = c("black", "red", "green", "purple")) + - scale_shape_manual(values = c(21, 17, 18, 19)) + + scale_shape_manual(values = c(21, 17, 18, 19)) + # each value corresponds to a shape labs(title = "Relationship between personal income and house assistance expenditure per region", x = "personal income (USD per capita)", y = "expenditure on housing assistance (USD per capita)", shape = "Region", color = "Region") + theme_minimal() +dev.off() diff --git a/problemSets/PS01/my_answers/PS01_DP.aux b/problemSets/PS01/my_answers/PS01_DP.aux index 9cdee9c..522d38c 100644 --- a/problemSets/PS01/my_answers/PS01_DP.aux +++ b/problemSets/PS01/my_answers/PS01_DP.aux @@ -3,5 +3,26 @@ \providecommand\HyField@AuxAddToFields[1]{} 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z*&wr(RAy&`%vOS(h6OTP=lvmj;EXd%8!mGPC6(D)b=u4}lRFO|@gje@XvPVM0q|~q z6-b)OKx1R4IVXwjOKz+cGx*ka==|ME&8ZlORg$+QN$YX&p1DfWM-2?>fptz9^!i?B z@F{?KVV;h?5Tn4{?2rK`5RK&Pf#jb=3zIZnk?H((}qp zelCzqW$@?Qq1)Z}|E@yCDih_l=Ksf-fBH z8!zwMQP93@eE9aU(bq4Ij`bV4Jbw2_o#)tKv*)b}lO1Etx#PpvbB{i$86cSDJ8O=; d={q($WOD3H*MVd2T8VK(*dXGJjmyMO{tX=bV+{ZR diff --git a/problemSets/PS01/my_answers/PS01_DP.tex b/problemSets/PS01/my_answers/PS01_DP.tex index 1680459..e627ce5 100644 --- a/problemSets/PS01/my_answers/PS01_DP.tex +++ b/problemSets/PS01/my_answers/PS01_DP.tex @@ -95,7 +95,10 @@ \newpage \section*{Solution - Question 1: Education} \vspace{.5cm} -\subsection*{1. Confidence Interval} +\subsection*{1. Confidence Interval for the Average Student IQ in the School} +\vspace{.5cm} +Since the sampling size is smaller than 30, we cannot assume that there is a normal sampling distribution. Instead, we will assume a t-distribution with 25-1 = 24 degrees of freedom (because the sample has n = 25 observations). \\[0.5cm] +The process for determining the confidence interval is outlined below: \begin{itemize} \item Calculate the mean @@ -104,7 +107,7 @@ \subsection*{1. Confidence Interval} [1] 98.44 \end{verbatim} \item - Calculate the sum of the squared errors to get the variance, and then the standard deviation + Calculate the sum of the squared errors to get the variance, and then the standard deviation (the square root of the variance) \lstinputlisting[language=R, firstline=43, lastline=47]{PS01_DP.R} \begin{verbatim} [1] 13.09287 @@ -116,11 +119,13 @@ \subsection*{1. Confidence Interval} [1] 2.618575 \end{verbatim} \item - Find the t-score for the desired confidence level, with 24 degrees of freedom + Find the t-score for the desired confidence level, with 24 degrees of freedom \\ + I calculated the t-score instead of a Z-score because the assumed sampling distribution is a t-distribution with 24 degrees of freedom. \lstinputlisting[language=R, firstline=54, lastline=55]{PS01_DP.R} \begin{verbatim} [1] 1.710882 \end{verbatim} + \newpage \item Construct the confidence interval by calculating its lower and upper limits \lstinputlisting[language=R, firstline=58, lastline=61]{PS01_DP.R} @@ -130,33 +135,38 @@ \subsection*{1. Confidence Interval} > upperlimit [1] 102.9201 \end{verbatim} + \item + \textbf{Conclusion:} The interval [93.96, 102.92] contains the true average of student IQs at the school (the true population mean) at least 90\% of the time, with repeated random sampling. \end{itemize} -\newpage +\vspace{1cm} \subsection*{2. Hypothesis Testing}\\ +\vspace{.5cm} \begin{itemize} - \item \textbf{Step 1:} assumptions\\ + \item \underline{\textbf{Step 1:} assumptions}\\ \begin{itemize} - \item the data is quantitative + \item the data is quantitative and continuous \item the sampling method is random - \item the sample size is smaller than 30, so we cannot assume it follows a normal distribution - therefore, I used the t-score and not the Z-score as the test statistic + \item the sample size is smaller than 30, so we assume it follows a t-distribution with 24 degrees of freedom and not a normal distribution; the test statistic that was calculated is a t-score \end{itemize} - \item \textbf{Step 2:} hypotheses\\ + \item \underline{\textbf{Step 2:} formulate hypotheses}\\ \begin{itemize} - \item \textbf{Null hypothesis:} the mean is lower or equal to 100 - \item \textbf{Alternative hypothesis:} the mean is higher than 100 + \item \textbf{Null hypothesis:} the average student IQ in the school (the mean) is lower than or equal to 100 + \item \textbf{Alternative hypothesis:} the average student IQ in the school (the mean) is higher than 100 \end{itemize} - \item \textbf{Step 3: } calculate the test statistic\\ + \item \underline{\textbf{Step 3: } calculate the test statistic : t-score}\\ \lstinputlisting[language=R, firstline=70, lastline=71]{PS01_DP.R} \begin{verbatim} [1] -0.5957439 \end{verbatim} - \item \textbf{Step 4:} calculate the p-value \\ - \lstinputlisting[language=R, firstline=74, lastline=75]{PS01_DP.R} +\newpage + \item \underline{\textbf{Step 4:} calculate the p-value}\\[0.5cm] + Because the hypothesis test that is carried out is one-sided, and the alternative hypothesis is that the true population mean is greater than 100, we are interested in the upper tail of the distribution. Hence, the lower.tail argument was set to FALSE. +\lstinputlisting[language=R, firstline=74, lastline=75]{PS01_DP.R} \begin{verbatim} [1] 0.7215383 \end{verbatim} - \item \textbf{Step 5:} draw a conclusion \\ - The p-value is higher than alpha, so we cannot reject the null hypothesis that the mean is lower or equal to 100 + \item\underline{\textbf{Step 5:} draw a conclusion}\\[0.5cm] + The p-value is much higher than the alpha value (0.05). Thus, we cannot reject the null hypothesis that the average student IQ in the school is lower than or equal to 100. The test result is not statistically significant. \end{itemize} \newpage @@ -178,7 +188,7 @@ \subsection*{2. Hypothesis Testing}\\ \vspace{.5cm} \noindent Explore the \texttt{expenditure} data set and import data into \texttt{R}. \vspace{.5cm} -\lstinputlisting[language=R, firstline=54, lastline=54]{PS01_DP.R} +\lstinputlisting[language=R, firstline=6, lastline=6]{PS01_DP.R} \vspace{.5cm} \begin{itemize} @@ -193,53 +203,87 @@ \subsection*{2. Hypothesis Testing}\\ \end{itemize} \newpage \section*{Solution - Question 2: Political Economy} + \subsection*{Plot the relationships among X1, X2, X3 and Y} +\lstinputlisting[language=R, firstline=96, lastline=103]{PS01_DP.R} +\vspace{.5cm} \begin{figure}[h!]\centering \caption{\footnotesize Scatterplot of X1 and Y} \label{fig:plot_1} - \includegraphics[width=.95\textwidth]{scatter_x1_y.png} + \includegraphics[width=.7\textwidth]{scatter_x1_y.png} \end{figure} -\textbf{Interpretation:} \\ There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\vspace{.5cm} +\underline{\textbf{Interpretation:}}\\[.3cm]There is a moderate positive association between the personal income and the expenditure on housing assistance per capita in a state. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. A positive linear pattern can also be distinguished by looking at the plot. \newpage +\lstinputlisting[language=R, firstline=107, lastline=114]{PS01_DP.R} +\vspace{.5cm} \begin{figure}[h!]\centering \caption{\footnotesize Scatterplot of X2 and Y} \label{fig:plot_2} - \includegraphics[width=.95\textwidth]{scatter_x2_y.png} + \includegraphics[width=.7\textwidth]{scatter_x2_y.png} \end{figure} -\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\vspace{.5cm} +\underline{\textbf{Interpretation:}}\\[.3cm] There is a moderate positive association between the number of "financially insecure" residents and the expenditure on housing assistance per capita in a state. The Pearson correlation coefficient suggests the same, as its value is above 0, but not above 0.5. Visually analysing the plot, there is an upward linear trend that can be identified, but there are many dots that fall outside of it, which suggests that the association is fairly weak. \newpage +\lstinputlisting[language=R, firstline=118, lastline=125]{PS01_DP.R} +\vspace{.5cm} \begin{figure}[h!]\centering \caption{\footnotesize Scatterplot of X3 and Y} \label{fig:plot_3} - \includegraphics[width=.95\textwidth]{scatter_x3_y.png} + \includegraphics[width=.7\textwidth]{scatter_x3_y.png} \end{figure} -\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\vspace{.5cm} +\underline{\textbf{Interpretation:}}\\[.3cm] There is a mild positive association also between the number of residents in urban areas and the expenditure on housing assistance per capita in a state. The value of the Pearson correlation coefficient is 0.46, suggesting a weak association between the two variables. There is a faint upward linear trend that can be observed from the plot, but the dots are very loosely grouped around it. \newpage +\lstinputlisting[language=R, firstline=129, lastline=136]{PS01_DP.R} +\vspace{.5cm} \begin{figure}[h!]\centering \caption{\footnotesize Scatterplot of X1 and X2} \label{fig:plot_4} - \includegraphics[width=.95\textwidth]{scatter_x1_x2.png} + \includegraphics[width=.7\textwidth]{scatter_x1_x2.png} \end{figure} -\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\vspace{.5cm} +\underline{\textbf{Interpretation:}}\\[.3cm] There doesn't seem to be a linear association between personal income per capita and the number of "financially insecure" residents within a state. The data points appear to be quite scattered in the graph, showing no clear linear trend. The Pearson correlation coefficient has a value of 0.21, indicating that we can only observe a very weak, if any, association between the two variables. \newpage +\lstinputlisting[language=R, firstline=140, lastline=147]{PS01_DP.R} +\vspace{.5cm} \begin{figure}[h!]\centering - \caption{\footnotesize Scatterplot of X2 and X3} + \caption{\footnotesize Scatterplot of X1 and X3} \label{fig:plot_5} - \includegraphics[width=.95\textwidth]{scatter_x2_x3.png} + \includegraphics[width=.7\textwidth]{scatter_x1_x3.png} \end{figure} -\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\vspace{.5cm} +\underline{\textbf{Interpretation:}}\\[.3cm] There is a moderate positive association between the personal income per capita and the number of urban residents in a state. The value of the Pearson correlation coefficient shows that these two variables have the strongest correlation within the dataset, but the value is still not high enough to indicate a strong association. Visually inspecting the plot, it can be observed that the dots follow an upward linear trend, but they are not very tightly grouped around it. \newpage +\lstinputlisting[language=R, firstline=151, lastline=158]{PS01_DP.R} +\vspace{.5cm} \begin{figure}[h!]\centering \caption{\footnotesize Scatterplot of X2 and X3} \label{fig:plot_6} - \includegraphics[width=.95\textwidth]{scatter_x2_x3.png} + \includegraphics[width=.7\textwidth]{scatter_x2_x3.png} \end{figure} -\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\vspace{.5cm} +\underline{\textbf{Interpretation:}}\\[.3cm] There doesn't seem to be a linear association between the number of "financially insecure" residents and the number of urban residents in a state. The dots are spread out quite evenly within the plot, without any distinguishable pattern. The Pearson correlation coefficient is quite close to 0, further indicating the absence of a meaningful association between the two variables. \newpage +\subsection*{Plot the relationship between Y and Region} +\lstinputlisting[language=R, firstline=170, lastline=178]{PS01_DP.R} +\vspace{.5cm} \begin{figure}[h!]\centering - \caption{\footnotesize Scatterplot of X1 and X2} + \caption{\footnotesize Boxplot of Y and Region} \label{fig:plot_7} - \includegraphics[width=.95\textwidth]{boxplot_reg_y.png} + \includegraphics[width=.7\textwidth]{boxplot_reg_y.png} \end{figure} -\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\vspace{.5cm} +\underline{\textbf{Interpretation:}}\\[.3cm] In order to visualize the average expenditure on housing assistance in each region, I generated a boxplot. This type of plot was chosen because it shows the distribution of data for each region, indicating the median but also the variability of the values. \\ It can be observed that the West region has the highest median for expenditure on housing assistance per capita and its interquartile range starts and ends at higher values than the others. Thus, the West spends on average the most out of the regions to provide housing assistance. +\newpage +\subsection*{Plot the relationship between Y, X1 and Region } +\lstinputlisting[language=R, firstline=184, lastline=195]{PS01_DP.R} +\vspace{.5cm} +\begin{figure}[h!]\centering + \caption{\footnotesize Scatterplot of X1, Y and Region} + \label{fig:plot_8} + \includegraphics[width=.7\textwidth]{scatter_x1_y_reg.png} +\end{figure} +\vspace{.5cm} +\underline{\textbf{Interpretation:}}\\[.3cm] In the previous plot of personal income and expenditure on housing assistance per capita in a state (Figure 1), a moderate positive association between the two was identified. This plot highlighting the values from different regions adds a new layer of interpretation. \\ Most notably, the South region shows on average both low income and low expenditure on housing assistace. The North Central region seems to also have mostly values for personal income that are proportional with the expenditure on housing assistance, the observations being concetrated towards the centre of the plot. Nevertheless, the West region shows some contrast in terms of expenditure on housing assistance for similar personal income values. This suggests that factors at the regional level might be correlated with both the housing assistance expenditure and the personal income per capita, and the association between the two of them might require further consideration and assessment. \end{document} diff --git a/problemSets/PS01/my_answers/scatter_x1_y.pdf b/problemSets/PS01/my_answers/scatter_x1_y.pdf deleted file mode 100644 index a481a90ab280b3738a6b94d1b0825f1bbb56ab8b..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 30382 zcmcHhWmr|;_r{IV9STTycO%_Mx0E2=f^3`mr>U-hjX{b52M33(q$sBi2L}&@eW9U%p9GAz zCBeZV;n>T{YC6a&$T~YZyFGO=x3pHUcCvP}x71dUfrAr@j@C7{BiAL6NN=oWqyG^$ zURW59b1RToI+y87jB_5{Zo>A3!#xlDUTzUAwDdlm@-=?5J}&;;n6Q3n&v zi;~?)j!!k3pOC_s&qpp5a>t0!w;TDYn-dxwS_gk$tYz#6uFt#g&11$jup1@MGa#^& zmUFEBT&nI}>+Tlu=m;3W4jAEJi%DWlVuUAK?rfjg-KXxEpZZgOc4xa?uBib3cJ9q| zsn7uJk~Q4zqi;ow zmb@78AX|6kx5wKGPW$R_5ALiR?a>eE;EbDF-nd~LN_1Q5zG@-g@F@NwI0|9=JpR%4 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z`5z$o+n@jX?$>vJ{Y`27`t|Djk2inH=FMLppI@%-fqnnxKRtebc$pS}-~7phDd(S_ Xub*zey?noa|K|SzE#Vh~fLj3ozpOQS diff --git a/problemSets/PS01/my_answers/PS01_DP.tex b/problemSets/PS01/my_answers/PS01_DP.tex index 33aee83..1680459 100644 --- a/problemSets/PS01/my_answers/PS01_DP.tex +++ b/problemSets/PS01/my_answers/PS01_DP.tex @@ -94,6 +94,71 @@ \newpage \section*{Solution - Question 1: Education} +\vspace{.5cm} +\subsection*{1. Confidence Interval} +\begin{itemize} + \item + Calculate the mean + \lstinputlisting[language=R, firstline=39, lastline=40]{PS01_DP.R} + \begin{verbatim} + [1] 98.44 + \end{verbatim} + \item + Calculate the sum of the squared errors to get the variance, and then the standard deviation + \lstinputlisting[language=R, firstline=43, lastline=47]{PS01_DP.R} + \begin{verbatim} + [1] 13.09287 + \end{verbatim} + \item + Calculate the standard error + \lstinputlisting[language=R, firstline=50, lastline=51]{PS01_DP.R} + \begin{verbatim} + [1] 2.618575 + \end{verbatim} + \item + Find the t-score for the desired confidence level, with 24 degrees of freedom + \lstinputlisting[language=R, firstline=54, lastline=55]{PS01_DP.R} + \begin{verbatim} + [1] 1.710882 + \end{verbatim} + \item + Construct the confidence interval by calculating its lower and upper limits + \lstinputlisting[language=R, firstline=58, lastline=61]{PS01_DP.R} + \begin{verbatim} + > lowerlimit + [1] 93.95993 + > upperlimit + [1] 102.9201 + \end{verbatim} + \end{itemize} +\newpage +\subsection*{2. Hypothesis Testing}\\ +\begin{itemize} + \item \textbf{Step 1:} assumptions\\ + \begin{itemize} + \item the data is quantitative + \item the sampling method is random + \item the sample size is smaller than 30, so we cannot assume it follows a normal distribution - therefore, I used the t-score and not the Z-score as the test statistic + \end{itemize} + \item \textbf{Step 2:} hypotheses\\ + \begin{itemize} + \item \textbf{Null hypothesis:} the mean is lower or equal to 100 + \item \textbf{Alternative hypothesis:} the mean is higher than 100 + \end{itemize} + \item \textbf{Step 3: } calculate the test statistic\\ + \lstinputlisting[language=R, firstline=70, lastline=71]{PS01_DP.R} + \begin{verbatim} + [1] -0.5957439 + \end{verbatim} + \item \textbf{Step 4:} calculate the p-value \\ + \lstinputlisting[language=R, firstline=74, lastline=75]{PS01_DP.R} + \begin{verbatim} + [1] 0.7215383 + \end{verbatim} + \item \textbf{Step 5:} draw a conclusion \\ + The p-value is higher than alpha, so we cannot reject the null hypothesis that the mean is lower or equal to 100 +\end{itemize} + \newpage \section*{Question 2: Political Economy} @@ -113,7 +178,7 @@ \vspace{.5cm} \noindent Explore the \texttt{expenditure} data set and import data into \texttt{R}. \vspace{.5cm} -\lstinputlisting[language=R, firstline=54, lastline=60]{PS01_DP.R} +\lstinputlisting[language=R, firstline=54, lastline=54]{PS01_DP.R} \vspace{.5cm} \begin{itemize} @@ -128,5 +193,53 @@ \end{itemize} \newpage \section*{Solution - Question 2: Political Economy} +\begin{figure}[h!]\centering + \caption{\footnotesize Scatterplot of X1 and Y} + \label{fig:plot_1} + \includegraphics[width=.95\textwidth]{scatter_x1_y.png} +\end{figure} +\textbf{Interpretation:} \\ There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\newpage +\begin{figure}[h!]\centering + \caption{\footnotesize Scatterplot of X2 and Y} + \label{fig:plot_2} + \includegraphics[width=.95\textwidth]{scatter_x2_y.png} +\end{figure} +\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\newpage +\begin{figure}[h!]\centering + \caption{\footnotesize Scatterplot of X3 and Y} + \label{fig:plot_3} + \includegraphics[width=.95\textwidth]{scatter_x3_y.png} +\end{figure} +\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\newpage +\begin{figure}[h!]\centering + \caption{\footnotesize Scatterplot of X1 and X2} + \label{fig:plot_4} + \includegraphics[width=.95\textwidth]{scatter_x1_x2.png} +\end{figure} +\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\newpage +\begin{figure}[h!]\centering + \caption{\footnotesize Scatterplot of X2 and X3} + \label{fig:plot_5} + \includegraphics[width=.95\textwidth]{scatter_x2_x3.png} +\end{figure} +\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\newpage +\begin{figure}[h!]\centering + \caption{\footnotesize Scatterplot of X2 and X3} + \label{fig:plot_6} + \includegraphics[width=.95\textwidth]{scatter_x2_x3.png} +\end{figure} +\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. +\newpage +\begin{figure}[h!]\centering + \caption{\footnotesize Scatterplot of X1 and X2} + \label{fig:plot_7} + \includegraphics[width=.95\textwidth]{boxplot_reg_y.png} +\end{figure} +\textbf{Interpretation:} There is a moderate positive association between the personal income and the expenditure on housing assistance in a state, both measured in USD per capita. The Pearson correlation coefficient points towards the same conclusion, as its value is above 0, but not close enough to 1 to suggest a strong association between the two variables. \end{document} diff --git a/problemSets/PS01/my_answers/boxplot_reg_y.png b/problemSets/PS01/my_answers/boxplot_reg_y.png new file mode 100644 index 0000000000000000000000000000000000000000..8d5c3fef9ede5ae57345cae1ad304425c1727aa8 GIT binary patch literal 23683 zcmeFZbySsW_cppHK|nwSQ53!fs#`(rLf1ESUAMEXdwVt@2dCz%W*SzL>CoL&_4wnoUg+iSZdGb&Og+d!e zesIpfZ=5@;gHb3<0)qz+q>Ua3KQJ>kvygrHLQ6+j$5h9{KubpWJ_>c$$46dO|C&58 ze`Hw!!_8*T&gA3(fSN+q6It3|7apK}BGxQB~96&Y!3ym#JaP#bG@E zQbv`KVQO?nvTUZwjN!^}{`zC0j>& zbJ^0uXm5vJ_h#O0{AWxDbx2Z|uj+;=wD;p|kLLE-Z@k7)lw%jZ7NHa`#}F>(w}gLW zd#nD4kv9Fq;kSXe*i%%S&oHqqmj`_BainI^{nPZQfiojQlB%Q1bI-N-(U8%%0Z%Ev z0#;|@5scE!P696qU77Prw=+28wdImf_t=vhv?}Zo_y~kJ2E2Qv$Q%s8qy?>z2R6<-&&F7^S zg>UtP)p~zp*G4fq9A_+mn-q`i12v06(aQZFu8Ku8iA3tfR<3?ygFhq&0vpj{YhuYJ 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